Among the biggest clichés in basketball, I think, is "rebounding wins games." I have a sneaking suspicion, though, that rebounding's link to winning is more correlation than causation — a byproduct of playing well.
We might try to calculate the direct correlation between total rebounding and winning to test the adage (to use a small sample, of the 16 playoff teams in 2011-12, 10 were in the top half of the league in total rebounding). Perhaps a better measure would be rebounding differential: of the 16 playoff teams, 11 were in the top half of the league.
I suspect, though, that using rebounding as a predictor of winning would, in an OLS-type regression, produce a biased estimate.* If we assume that defensive rebounding is much easier than offensive rebounding, or at least more likely, we should assume that rebounding is highly correlated with defensive field goal percentage (or, to be more accurate, rebounding differential is highly correlated with the disparity between offensive and defensive field goal percentage) — which would be either an omitted variable in a regression or, if included, a variable strongly correlated with another variable.
The basic idea I'm getting at here is that a team has a big advantage rebounding at the defensive end, so if it can get the other team to miss a lot of shots, it's going to get a lot of rebounds. Conversely, if the team simultaneously makes a high percentage of its own shots, it's going to limit the other team's opportunity to rebound, and it's going to be in good position to lead in rebounding differential — and on the scoreboard. My point isn't that rebounding won't show up in the win total; it's that there is so much other stuff getting caught up in that rebounding stat that it's not accurately describing the causes of winning and getting undue weight as a factor.
The one thing that I'm really missing is rate of play, or pace; that is, some teams put up a lot more shots in a game than another. Let's say a team shoots .500 while putting up 77.1 shots a game (the league low last year); it's creating 38.55 opportunities for a rebound**. A team putting up 86.5 shots a game (the league high) only has to shoot .446 to create the same number of opportunities. This will complicate our total rebounding numbers, and if a relatively slow team meets a relatively fast team, it could complicate our differential numbers as well.
Still, I think the main point is sound: if you shoot well and make the other team shoot poorly, you should expect to lead in rebounds, and you should expect to win — not because of the rebounding differential but because of how your teams played relatively on offense (or defense).
The idea came to me, sadly enough, while I was playing a video game. I had been noticing that although my team did not possess many great rebounders (Kevin Love excepted) and ranked pretty poorly in leaguewide rebound totals, it consistently outrebounded its opponents in individual games. That turned out not to be so surprising a result: I was leading the league in both field goal percentage and field goal percentage against.
Rebounding has been listed as one of the four factors of basketball success (along with shooting, turnovers and free throws). The other three, however, seem to be independent variables. So while rebounding may on its own appear to be a better explanation of success than free throws, it might, in conjunction with other variables, lessen the significance of a prediction. Rebounds, as I see them, are something like a necessary, but not sufficient, condition of winning — you need them, but mostly because they tell you that you're doing other stuff right.
* - I should note that I currently do not have access to OLS software and am going almost entirely off intuition here. This is one of the reasons that I'm trying not to use many examples from real life here; without a more complete statistical analysis, the numbers are hard to interpret, and what seems like a high (or low) correlation may not be borne out under more rigorous analysis.
** - I'm ignoring free throws for simplicity's sake.
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